Some of the UK's best mathematicians head to Government Communications Headquarters (GCHQ) and code breaking in Cheltenham after university.

But just what kind of skills are needed for the job and what makes a top brass code breaker these days?

So much of code breaking is counter-intuitive

Simon Singh, author

GCHQ is referred to by locals in Cheltenham as "our secret neighbour" and they are not known for handing out detailed information about what they are working on right now.

However, according to a GCHQ spokesperson: "We look for analytical and lateral minded people with first or second class honours degrees from university in mathematics, statistics or computer science.

"A masters or PhD will give you additional credit."

"A good university background in pure mathematics is a must, along with a talent with algebra.

"At GCHQ we have the highest concentration of pure mathematicians in the country."

Obsession and precision

A proven understanding of finite field theory - otherwise known as Galois field theory - is recommended, too.

But, according to Simon Singh, science commentator and author of the acclaimed Code Book, obsession and precision as well as a counter intuitive mind is a big help if you want to crack the big ones.

Code breakers were based at Bletchley Park during World War II

Speaking at the Cheltenham Festival of Science this week, Dr Singh said: "That's what attracted me to writing a book about codes; so much of code breaking is counter-intuitive. That makes it exciting."

A great deal of "ingenuity and determination" is needed as well, said Adam Wheeler, dean of the faculty of mathematical studies, University of Southampton.

The university recently ran a cipher challenge for under-19-year-olds, based on the original challenge published by Dr Singh.

The university cipher texts were cracked by school students within hours of the competition being announced. Another competition is set for the end of next year.

Cryptography

However, Dr Singh's codes in his Code Book were a little more difficult to crack.

They were eventually broken by a Swedish team in October 2000 after one year and one month.

Code breaking skills are still a very practical and necessary requirement for intelligence organisations such as GCHQ.

"Cryptography is more important today than ever before. We live in an information age and one of the best ways to protect information is to encrypt it," said Dr Singh.

Modern day encryption software now incorporated in most commercial e-mail and web-browser programs is probably being used by many terrorist organisations.

Human error

But the way so many codes are broken today - just as they were back in the pioneering days at Bletchley Park in World War II - is that people make mistakes. It is human fallibility which gives the game away.

Dr Singh agrees whole-heartedly with this. In fact, it was his fallibility which led to him giving away £10,000 in his cipher competition.

Until recently, the basis of code breaking has depended on the transfer of mathematical keys to unlock a code.

Codes have moved on since the days of the Enigma machin

Today, it is more likely that organisations communicating with each other transfer padlocks to a code and you keep your own keys.

Dr Singh used the triple DES or Data Encryption Standard system for his encryption. This is a mainstay of encoding for commercial electronic traffic such as bank transfers.

It is based on the principle that a code is electronically padlocked by a user and sent to whoever they want to communicate with.

The receiver then padlocks the code with their own padlock and sends it back, so that now the code has two padlocks on it.

Then the original sender unlocks their padlock and sends it to the original receiver. The code at this stage has the receiver's own padlock on it which they can open.

Triple exchange

It is a principle of triple exchange.

But instead of encoding with one padlock, decoding with two and then encoding with one, Dr Singh encoded with two and decoded with one and encoded with two, allowing his code to be cracked.

Today, one of the biggest questions facing code breakers is weighing up the difference between practically and theoretically uncrackable codes.

"Practically, triple DES is uncrackable but there are other codes such as quantum codes that are theoretically uncrackable," said Dr Singh.

"If quantum codes were eventually cracked, it would mean physics would be turned on its head.

"I very much doubt this would happen. A lot of scientists would have a lot to answer for our current understanding of science.

"But I guess the Enigma code encryptors thought this too at the beginning of World War II," he said.

So maybe to become a top notch code breaker these days you not only need a passion for pure maths, but also a good understanding of human fallibility. Just like in the good old days.